Club captain Paul Hanlon, first-choice goalkeeper Matt Macey, and influential midfielder Joe Newell were all involved in preparations for the trip to North Lanarkshire on Friday at the club’s Ormiston training base.
Chris Mueller, who missed the goalless draws against Dundee and St Johnstone through illness, was also training with the group at the Hibernian Training Centre.
However, Sunday’s game may come too soon for some.
Newell – who had a bandage on his left knee – has been all but ruled out of the last-eight encounter, with the Scottish Premiership trip to Aberdeen on March 19 pencilled in as a possible comeback for the 28-year-old.
The other players are likely to be assessed on a game-by-game basis. Maloney gives his squad until the last possible moment to prove their fitness ahead of a match but with some vital league games coming back he is unlikely to rush anyone back into action before they are ready.
Harry Clarke, Kyle Magennis, Demi Mitchell, Paul McGinn, and Kevin Nisbet remain sidelined for the Capital club.
Maloney was hopeful last month that defender Clarke – who is yet to kick a ball for Hibs since joining on an 18-month loan deal in January after he suffered a hamstring injury in training – could be in contention either before or after the international break.
McGinn, meanwhile, returned from an initial injury in the 2-0 defeat by Rangers at Ibrox last month only to break down after just 12 minutes.